David Moyes was not exactly singing from the same hymn sheet as the travelling fans who chanted "We're gonna win the league", but the fact that the Everton manager said he would be happy to sit among those supporters provided a ringing endorsement of his team. "I said to the players afterwards: 'I'm enjoying watching you play,' " he added. "There were times at this point last season when I wouldn't have paid to watch. I would definitely pay to come and watch us now."

These are exciting times at Everton. A return of 10 points from five matches, on the back of a strong finish to last season, has put a spring in Moyes's step and fuelled belief among the players that something special can be achieved this term. The squad look far stronger than in previous years, Everton have no European football to serve as a distraction, and there is a confidence about the players that comes with a prolonged run of decent results.

This third league win of the season, courtesy of goals from Victor Anichebe, Kevin Mirallas and Marouane Fellaini, means only the two Manchester clubs have picked up more points than Everton in 2012.

"It's as good an Everton side as I've played in," said the left-back Leighton Baines. "The last time we were at this level was the year we got to the cup final [2009]. We had a really strong squad then, it got broken up a bit in between, but we're getting back to that level.

"We've seen times where numbers have been thin and we've had to play young lads. Now we can call on experienced, seasoned professionals [who] would be playing in most other teams. That strength in depth is something we haven't had before. Victor [Anichebe] highlights that — he's been on the bench but has come in and shown what a good player he is. If we can get him playing like that every week, people will bevery scared."

There was certainly a feeling of trepidation in the Swansea defence on Saturday — Everton had 30 attempts on goal. Although Nathan Dyer's sending off hardly helped, Everton had been opening up Michael Laudrup's side with ease long before the substitute was shown two yellow cards in less than three minutes.

Alan Tate, who was substituted in the second half, was scathing in his criticism of his Swansea team-mates. "It was disappointing but that's what happens if you play as a group of individuals rather than a team," he said. "We have gone away from the team aspect which made us good last season. We need to get back to playing as a team, otherwise we're going to struggle like that every week.

"Defensively we tried to do it on our own. We were more concerned with scoring goals than we were about stopping them at the other end. We were gung-ho really. Everyone was going forwards, leaving the back four to defend by themselves. You can't do that in any league, let alone this league. We haven't got the players that Everton have got.

"We can't get away from the fact that defensively we weren't good enough – that's not just the back four, it's the whole team. They played the ball forwards to two big lads, and we didn't have people getting around them and coming in from the front. All the lads have trained with us so they know what's [being] asked of them. But if people are going to play individually we may as well pack up now."